The GCN [1]} is arguably the most widely-used neural network architecture on graphs.
Consider a graph \(\mathcal {G}\)  comprised of \(n\)  nodes with \(d\) -dimensional features \(\mathbf {X} \in \mathbb {R}^{n \times d}\) .
The output \(\mathbf {Y} \in \mathbb {R}^{n \times d^{\prime }}\)  of a GCN can be expressed as \(\mathbf {Y} = \Psi _{\mathcal {G}}(\mathbf {X}; \Theta )\) , where \(\Psi _{\mathcal {G}}\)  is a layered architecture with trainable parameters \(\Theta \) .
If we define \(\mathbf {H}_0 = \mathbf {X}\) , we then have that \(\mathbf {Y} = \Psi _{\mathcal {G}}(\mathbf {X}; \Theta ) = \mathbf {H}_L\) , where an intermediate \(\ell \) -th layer of the GCN is given by
\(\mathbf {H}_{\ell +1} = \sigma (\bar{\mathbf {A}} \, \mathbf {H}_\ell \, \Theta _\ell ).\) 
